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Abstract

Liquid droplets on rough hydrophobic substrates are typically observed either in the Cassie/Baxter (or “fakir”) state, i.e. on top of the roughness structures [1], or in the Wenzel state, where the droplet completely wets the substrate [2]. While virtually all studies hitherto have been considering droplets much larger than the roughness scale of the substrate [3], we, for the first time, investigate the case where the size of the droplet is comparable to the surface sperities. This is a very natural situation that occurs whenever a liquid drop condenses or evaporates on such a substrate. We find a new stable state where the droplet is partially impaled, not yet contacting the bottom surface. The penetration depth decreases upon evaporation, leading to a qualitatively new self-cleaning mechanism. We demonstrate the generic character of this finding and emphasize its scale invariance, both being issues of considerable importance for practical applications.